论文标题
图同态卷积
Graph Homomorphism Convolution
论文作者
论文摘要
在本文中，我们从图形同态的角度研究了图分类问题。我们认为同态从$ f $到$ g $，其中$ g $是利益的图表（例如分子或社交网络），$ f $属于某些图形（例如路径或非同构树）。我们表明，图形同态数字提供了一个天然不变的（同构不变性和$ \ MATHCAL {F} $ - 不变的）嵌入地图，可用于图形分类。通过$ \ mathcal {f} $来查看图形分类器的表达能力 - 难以区分的概念，我们证明了图形同态向量的通用性属性，以近似$ \ mathcal {f} $ - 不变函数。实际上，通过选择$ \ Mathcal {f} $的元素有限制的树宽，我们表明同构方法与其他方法相比是有效的。
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $\mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $\mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $\mathcal{F}$-invariant functions. In practice, by choosing $\mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods.
